A body moves with a velocity of $2\, m s ^{-1}$ for $5\, s$, then its velocity increases uniformly to $10\, m s ^{-1}$ in next $5\, s.$ Thereafter, its velocity begins to decrease at a uniform rate until it comes to rest after $5\, s$.

$(i)$ Plot a velocity-time graph for the motion of the body.

$(ii)$ From the graph, find the total distance covered by the body after $2\, s$ and $12\, s$.

The area under the velocity$-$time graph gives the value of

The $v-t$ graph of cars $A$ and $B$ which start from the same place and move along straight road in the same direction, is shown. Calculate

$(i)$ the acceleration of car $A$ between $0$ and $8\, s$.

$(ii)$ the acceleration of car $B$ between $2\, s$ and $4\, s$.

$(iii)$ the points of time at which both the cars have the same velocity.

$(iv)$ which of the two cars is ahead after $8\, s$ and by how much ?

Can the distance travelled by a particle be zero when displacement is not zero ?

For the motion on a straight line path with constant acceleration the ratio of the maqnitude of the displacement to the distance covered is